24740 + Interview Questions in Mathematics

1.	Question 7Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
Answer» Question 7 Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

Discussion

2.	There are seven equal chords in the circle with centre O in the given figure. The value of x will be ?
Answer» There are seven equal chords in the circle with centre O in the given figure. The value of x will be ?

Discussion

3.	Write the complement of an angle of measure x°.
Answer» Write the complement of an angle of measure x°.

Discussion

4.	The simplest rationalising factor of 25−3 is(a) 25+3(b) 25+3(c) 5+3(d) 5-3
Answer» The simplest rationalising factor of $2 \sqrt{5}$ − $\sqrt{3}$ is (a) $2 \sqrt{5} + 3$ (b) $2 \sqrt{5} + \sqrt{3}$ (c) $\sqrt{5} + \sqrt{3}$ (d) $\sqrt{5} - \sqrt{3}$

Discussion

5.	Find the length of the side of a cube whose total surface area is 1536 cm2.
Answer» Find the length of the side of a cube whose total surface area is $1536 c m^{2}$ .

Discussion

6.	The difference between two numbers is 70. The numbers are in ratio 5:3. Let the numbers be x and y (x > y). Select the correct equations.
Answer» The difference between two numbers is 70. The numbers are in ratio 5:3. Let the numbers be x and y (x > y). Select the correct equations.

Discussion

7.	Question 13(ii)The following are the ages of 300 patients getting medical treatment in a hospital on a particular dayAge(in year)10−2020−3030−4040−5050−6060−70Number of patients604255705320Form (ii) More than type cumulative frequency distribution.
Answer» Question 13(ii) The following are the ages of 300 patients getting medical treatment in a hospital on a particular day $\begin{matrix} A g e (i n y e a r) & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 N u m b e r o f p a t i e n t s & 60 & 42 & 55 & 70 & 53 & 20 \end{matrix}$ Form (ii) More than type cumulative frequency distribution.

Discussion

8.	A concrete pillar has a radius of 3.5 cm and a length of 15 cm. The total surface area of the pillar is ______.
Answer» A concrete pillar has a radius of 3.5 cm and a length of 15 cm. The total surface area of the pillar is ______.

8.

A concrete pillar has a radius of 3.5 cm and a length of 15 cm. The total surface area of the pillar is ______.

Answer»

A concrete pillar has a radius of 3.5 cm and a length of 15 cm. The total surface area of the pillar is ______.

Discussion

9.	Question 31Expand the following:(i) (3a–2b)3(ii) (1x+y3)3(iii) (4−13x)3
Answer» Question 31 Expand the following: (i) $(3 a - 2 b)^{3}$ (ii) ${(\frac{1}{x} + \frac{y}{3})}^{3}$ (iii) ${(4 - \frac{1}{3 x})}^{3}$

Discussion

10.	Question 1Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
Answer» Question 1 Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Discussion

11.	A solid cylinder of length L & radius r is heat up to same temperature as that of a cube of edge length a . If both have same material, same volume & allowed to cool under similar conditions, then ratio of amount of radiatins radiated will be what?
Answer» A solid cylinder of length L & radius r is heat up to same temperature as that of a cube of edge length a . If both have same material, same volume & allowed to cool under similar conditions, then ratio of amount of radiatins radiated will be what?

Discussion

12.	The product of two whole numbers is always a:
Answer» The product of two whole numbers is always a:

Discussion

13.	Question 131√9−√8 is equal to A) 12(3−2√2)B) 13+2√2C) 3−2√2D) 3+2√2
Answer» Question 13 $\frac{1}{\sqrt{9} - \sqrt{8}}$ is equal to A) $\frac{1}{2} (3 - 2 \sqrt{2})$ B) $\frac{1}{3 + 2 \sqrt{2}}$ C) $3 - 2 \sqrt{2}$ D) $3 + 2 \sqrt{2}$

Discussion

14.	Diagonal AC and BD of quadrilateral ABCD intersects each other at point O. Prove that AB + BC + CD + AD < 2 (AC + BD).
Answer» Diagonal AC and BD of quadrilateral ABCD intersects each other at point O. Prove that AB + BC + CD + AD < 2 (AC + BD).

14.

Diagonal AC and BD of quadrilateral ABCD intersects each other at point O. Prove that AB + BC + CD + AD < 2 (AC + BD).

Answer»

Diagonal AC and BD of quadrilateral ABCD intersects each other at point O.

Prove that AB + BC + CD + AD < 2 (AC + BD).

Discussion

15.	If AB = QR, BC = PR and CA = PQ, then triangle _________ ≅ triangle _________.
Answer» If AB = QR, BC = PR and CA = PQ, then triangle _________ ≅ triangle _________.

Discussion

16.	Let ab denote the length of the hypotenuse of a right angle triangle whose remaining two sides have length a, b. If (1216)*k=25 then find the value of k2.
Answer» Let ab denote the length of the hypotenuse of a right angle triangle whose remaining two sides have length a, b. If (1216)*k=25 then find the value of k2.

Discussion

17.	Amita and Balu applied for a typing job. Amita can type 120 words per minute, while Balu can type 80 words in 50 seconds. The employer wants to select the one with the fastest typing speed. Who would get the job?
Answer» Amita and Balu applied for a typing job. Amita can type $120$ words per minute, while Balu can type $80$ words in $50$ seconds. The employer wants to select the one with the fastest typing speed. Who would get the job?

Discussion

18.	For any positive real number x, write the value of {(xa)b}1ab{(xb)c}1bc{(xc)a}1ca
Answer» For any positive real number x, write the value of ${(x^{a})^{b}}^{\frac{1}{a b}} {(x^{b})^{c}}^{\frac{1}{b c}} {(x^{c})^{a}}^{\frac{1}{c a}}$

18.

For any positive real number x, write the value of {(xa)b}1ab{(xb)c}1bc{(xc)a}1ca

Answer»

For any positive real number x, write the value of

${(x^{a})^{b}}^{\frac{1}{a b}} {(x^{b})^{c}}^{\frac{1}{b c}} {(x^{c})^{a}}^{\frac{1}{c a}}$

Discussion

19.	If one of the four angles formed by two intersecting lines is a right angle, then show that each of the four angles is a right angle.
Answer» If one of the four angles formed by two intersecting lines is a right angle, then show that each of the four angles is a right angle.

Discussion

20.	Question 100Divide 293 by 1000000 and express the result in standard form:
Answer» Question 100 Divide 293 by 1000000 and express the result in standard form:

20.

Question 100Divide 293 by 1000000 and express the result in standard form:

Answer»

Question 100

Divide 293 by 1000000 and express the result in standard form:

Discussion

21.	Question 1 (iv)Classify 1√2 as rational or irrational.
Answer» Question 1 (iv) Classify $\frac{1}{\sqrt{2}}$ as rational or irrational.

Discussion

22.	A tree is broken at a height of 5 m from the groundand its top touches the ground at a distance of12 m from the base of the tree. Find the originalheight of the tree.
Answer» A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

Discussion

23.	. Find the percentage increase in the area of a triangle if its each side is tripled.
Answer» . Find the percentage increase in the area of a triangle if its each side is tripled.

Discussion

24.	What is the maximum number of common tangents that can be drawn to two circles of different radii, touching each other internally?
Answer» What is the maximum number of common tangents that can be drawn to two circles of different radii, touching each other internally?

Discussion

25.	39 ABCD is a cyclic quadrilateral whose diagonals AC and BD intersect at P.If AB = DC,then prove that triangle PAB is congurence to triangle PDC
Answer» 39 ABCD is a cyclic quadrilateral whose diagonals AC and BD intersect at P.If AB = DC,then prove that triangle PAB is congurence to triangle PDC

Discussion

26.	Expressions that contain only two terms are known as:
Answer» Expressions that contain only two terms are known as:

Discussion

27.	Q 1 : what is enthalpy ? Q 2 : what is H ? What does it shows . And it's sign conventions.
Answer» Q 1 : what is enthalpy ? Q 2 : what is H ? What does it shows . And it's sign conventions.

Discussion

28.	Identify the polynomials in one variable.
Answer» Identify the polynomials in one variable.

Discussion

29.	Number of persons in various age groups in a town are represented by a bar graph. If all persons in the age group of 60 and above are called senior citizens. How many senior citizens are there in the town? Also find the two age groups who have the same population.
Answer» Number of persons in various age groups in a town are represented by a bar graph. If all persons in the age group of 60 and above are called senior citizens. How many senior citizens are there in the town? Also find the two age groups who have the same population.

Discussion

30.	The surface area of a cube of edge 1.5 cm is
Answer» The surface area of a cube of edge 1.5 cm is

Discussion

31.	Question 2 (iii)Write True or False. Give reasons for your answers.(iii) If a circle is divided into three equal arcs, each is a major arc.
Answer» Question 2 (iii) Write True or False. Give reasons for your answers. (iii) If a circle is divided into three equal arcs, each is a major arc.

Discussion

32.	A library charges Rs.5 for issuing a book for 1 day and Rs.1 per day thereafter. If ritu had taken a book for 5 days. What is the total amount she needs to pay.
Answer» A library charges Rs.5 for issuing a book for 1 day and Rs.1 per day thereafter. If ritu had taken a book for 5 days. What is the total amount she needs to pay.

Discussion

33.	The mean of 24 numbers is 35. If 3 is added to each number, what will be the new mean?
Answer» The mean of 24 numbers is 35. If 3 is added to each number, what will be the new mean?

Discussion

34.	A quadrilateral, ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively. If quadrilateral, ABCD is a parallelogram, what can you say about the quadrilateral, PQRS?
Answer» A quadrilateral, $A B C D$ is drawn in which the mid points of sides $A B, B C, C D$ and $A D$ are $P, Q, R$ and $S$ respectively. If quadrilateral, $A B C D$ is a parallelogram, what can you say about the quadrilateral, $P Q R S ?$

34.

A quadrilateral, ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively. If quadrilateral, ABCD is a parallelogram, what can you say about the quadrilateral, PQRS?

Answer»

A quadrilateral, $A B C D$ is drawn in which the mid points of sides $A B, B C, C D$ and $A D$ are $P, Q, R$ and $S$ respectively.

If quadrilateral, $A B C D$ is a parallelogram, what can you say about the quadrilateral, $P Q R S ?$

Discussion

35.	The points (a,a),(–a,−a) and (–√3a,√3a) are the vertices of a/an _____ triangle.
Answer» The points $(a, a), (- a, - a)$ and $(- \sqrt{3} a, \sqrt{3} a)$ are the vertices of a/an _____ triangle.

Discussion

36.	ABCD is a parallelogram. E and F are the mid-Points of BC and AD respectively. Show that the segments BF and DE trisect the diagonal AC. [4 MARKS]
Answer» ABCD is a parallelogram. E and F are the mid-Points of BC and AD respectively. Show that the segments BF and DE trisect the diagonal AC. [4 MARKS]

Discussion

37.	Find the value of 382−22216, using a suitable identity.
Answer» $Find the value of \frac{38^{2} - 22^{2}}{16}, using a suitable identity.$

Discussion

38.	A bus stop is barricated from the remaining part of the road, by using 50 hollow cones made of recycled card-board. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m2. What will be the cost of painting all these cones. (Use π = 3.14 and 1.04=1.02)
Answer» A bus stop is barricated from the remaining part of the road, by using 50 hollow cones made of recycled card-board. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m². What will be the cost of painting all these cones. (Use $π = 3.14$ and $\sqrt{1.04} = 1.02)$

Discussion

39.	In the figure, if l1\|\|l2, what x + y in terms of w and z ?
Answer» In the figure, if $l_{1} \| \| l_{2}$ , what x + y in terms of w and z ?

39.

In the figure, if l1||l2, what x + y in terms of w and z ?

Answer»

In the figure, if $l_{1} | | l_{2}$ , what x + y in terms of w and z ?

Discussion

40.	Given the zeroes of a cubic polynomial p(x)=3x3−10x2−27x+10 are 5, -2 and 13. Verify the relation between its zeros and coefficients.
Answer» Given the zeroes of a cubic polynomial $p (x) = 3 x^{3} - 10 x^{2} - 27 x + 10$ are 5, -2 and $\frac{1}{3}$ . Verify the relation between its zeros and coefficients.

Discussion

41.	In a quadrilateral MIST where MI = 3.5 cm, IS = 6.5 cm, ∠M = 75∘, ∠ I = 105∘ and ∠S = 120∘. Which line segment should be drawn first?
Answer» In a quadrilateral MIST where MI = 3.5 cm, IS = 6.5 cm, $∠$ M = $75^{\circ}$ , $∠$ I = $105^{\circ}$ and $∠$ S = $120^{\circ}$ . Which line segment should be drawn first?

Discussion

42.	Find the value of cos226∘+cos264∘sin255∘+sin235∘.1
Answer» Find the value of $\frac{c o s^{2} 26^{\circ} + c o s^{2} 64^{\circ}}{s i n^{2} 55^{\circ} + s i n^{2} 35^{\circ}} .$ 1

Discussion

43.	Question 123(i) Which of the following figure do not have line symmetry?
Answer» Question 123(i) Which of the following figure do not have line symmetry?

43.

Question 123(i) Which of the following figure do not have line symmetry?

Answer»

Question 123(i)
Which of the following figure do not have line symmetry?

Discussion

44.	In the given figure, ABCD, ABFE and CDEF are parallelograms. Prove thatar(Δ ADE) = ar(Δ BCF)
Answer» In the given figure, ABCD, ABFE and CDEF are parallelograms. Prove that ar(Δ ADE) = ar(Δ BCF)

Discussion

45.	Cost of 20 envelopes is Rs. 50. Then, how many envelopes can be purchased for 10 Rupees?
Answer» Cost of 20 envelopes is Rs. 50. Then, how many envelopes can be purchased for 10 Rupees?

Discussion

46.	Find the coordinates of the point where the line 2x-y=3 meets both the Axes
Answer» Find the coordinates of the point where the line 2x-y=3 meets both the Axes

Discussion

47.	if x=(10a)^-b*a^b where a,b,c are whole numbers and x is a terminating decimal number then x cannot be equal to
Answer» if x=(10a)^-b*a^b where a,b,c are whole numbers and x is a terminating decimal number then x cannot be equal to

Discussion

48.	Question 3 (ii)Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that:ΔABC≅ΔPQR
Answer» Question 3 (ii) Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that: $Δ A B C ≅ Δ P Q R$

Discussion

49.	Find the leftmost and the rightmost number when the following numbers are represented on the number line.−1910 ,−95−85−32−1710
Answer» Find the leftmost and the rightmost number when the following numbers are represented on the number line. $\frac{- 19}{10}, \frac{- 9}{5} \frac{- 8}{5} \frac{- 3}{2} \frac{- 17}{10}$

49.

Find the leftmost and the rightmost number when the following numbers are represented on the number line.−1910 ,−95−85−32−1710

Answer»

Find the leftmost and the rightmost number when the following numbers are represented on the number line.

$\frac{- 19}{10}, \frac{- 9}{5} \frac{- 8}{5} \frac{- 3}{2} \frac{- 17}{10}$

Discussion

50.	State the mid-points of all the sides in the figure.
Answer» State the mid-points of all the sides in the figure.

50.

State the mid-points of all the sides in the figure.

Answer»

State the mid-points of all the sides in the figure.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 7Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

There are seven equal chords in the circle with centre O in the given figure. The value of x will be ?

Write the complement of an angle of measure x°.

The simplest rationalising factor of 25−3 is(a) 25+3(b) 25+3(c) 5+3(d) 5-3

Find the length of the side of a cube whose total surface area is 1536 cm2.

The difference between two numbers is 70. The numbers are in ratio 5:3. Let the numbers be x and y (x &gt; y). Select the correct equations.

Question 13(ii)The following are the ages of 300 patients getting medical treatment in a hospital on a particular dayAge(in year)10−2020−3030−4040−5050−6060−70Number of patients604255705320Form (ii) More than type cumulative frequency distribution.

A concrete pillar has a radius of 3.5 cm and a length of 15 cm. The total surface area of the pillar is ______.

Question 31Expand the following:(i) (3a–2b)3(ii) (1x+y3)3(iii) (4−13x)3

Question 1Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

A solid cylinder of length L & radius r is heat up to same temperature as that of a cube of edge length a . If both have same material, same volume & allowed to cool under similar conditions, then ratio of amount of radiatins radiated will be what?

The product of two whole numbers is always a:

Question 131√9−√8 is equal to A) 12(3−2√2)B) 13+2√2C) 3−2√2D) 3+2√2

Diagonal AC and BD of quadrilateral ABCD intersects each other at point O. Prove that AB + BC + CD + AD &lt; 2 (AC + BD).

If AB = QR, BC = PR and CA = PQ, then triangle _________ ≅ triangle _________.

Let a*b denote the length of the hypotenuse of a right angle triangle whose remaining two sides have length a, b. If (12*16)*k=25 then find the value of k2.

Amita and Balu applied for a typing job. Amita can type 120 words per minute, while Balu can type 80 words in 50 seconds. The employer wants to select the one with the fastest typing speed. Who would get the job?

For any positive real number x, write the value of {(xa)b}1ab{(xb)c}1bc{(xc)a}1ca

If one of the four angles formed by two intersecting lines is a right angle, then show that each of the four angles is a right angle.

Question 100Divide 293 by 1000000 and express the result in standard form:

Question 1 (iv)Classify 1√2 as rational or irrational.

A tree is broken at a height of 5 m from the groundand its top touches the ground at a distance of12 m from the base of the tree. Find the originalheight of the tree.

. Find the percentage increase in the area of a triangle if its each side is tripled.

What is the maximum number of common tangents that can be drawn to two circles of different radii, touching each other internally?

39 ABCD is a cyclic quadrilateral whose diagonals AC and BD intersect at P.If AB = DC,then prove that triangle PAB is congurence to triangle PDC

Expressions that contain only two terms are known as:

Q 1 : what is enthalpy ? Q 2 : what is H ? What does it shows . And it's sign conventions.

Identify the polynomials in one variable.

Number of persons in various age groups in a town are represented by a bar graph. If all persons in the age group of 60 and above are called senior citizens. How many senior citizens are there in the town? Also find the two age groups who have the same population.

The surface area of a cube of edge 1.5 cm is

Question 2 (iii)Write True or False. Give reasons for your answers.(iii) If a circle is divided into three equal arcs, each is a major arc.

A library charges Rs.5 for issuing a book for 1 day and Rs.1 per day thereafter. If ritu had taken a book for 5 days. What is the total amount she needs to pay.

The mean of 24 numbers is 35. If 3 is added to each number, what will be the new mean?

A quadrilateral, ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively. If quadrilateral, ABCD is a parallelogram, what can you say about the quadrilateral, PQRS?

The points (a,a),(–a,−a) and (–√3a,√3a) are the vertices of a/an _____ triangle.

ABCD is a parallelogram. E and F are the mid-Points of BC and AD respectively. Show that the segments BF and DE trisect the diagonal AC. [4 MARKS]

Find the value of 382−22216, using a suitable identity.

In the figure, if l1||l2, what x + y in terms of w and z ?

Given the zeroes of a cubic polynomial p(x)=3x3−10x2−27x+10 are 5, -2 and 13. Verify the relation between its zeros and coefficients.

In a quadrilateral MIST where MI = 3.5 cm, IS = 6.5 cm, ∠M = 75∘, ∠ I = 105∘ and ∠S = 120∘. Which line segment should be drawn first?

Find the value of cos226∘+cos264∘sin255∘+sin235∘.1

Question 123(i) Which of the following figure do not have line symmetry?

In the given figure, ABCD, ABFE and CDEF are parallelograms. Prove thatar(Δ ADE) = ar(Δ BCF)

Cost of 20 envelopes is Rs. 50. Then, how many envelopes can be purchased for 10 Rupees?

Find the coordinates of the point where the line 2x-y=3 meets both the Axes

if x=(10a)^-b*a^b where a,b,c are whole numbers and x is a terminating decimal number then x cannot be equal to

Question 3 (ii)Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that:ΔABC≅ΔPQR

Find the leftmost and the rightmost number when the following numbers are represented on the number line.−1910 ,−95−85−32−1710

State the mid-points of all the sides in the figure.

The difference between two numbers is 70. The numbers are in ratio 5:3. Let the numbers be x and y (x > y). Select the correct equations.

Diagonal AC and BD of quadrilateral ABCD intersects each other at point O. Prove that AB + BC + CD + AD < 2 (AC + BD).

If AB = QR, BC = PR and CA = PQ, then triangle _ ≅ triangle _.

Let ab denote the length of the hypotenuse of a right angle triangle whose remaining two sides have length a, b. If (1216)*k=25 then find the value of k2.